The Chinese Generals Problem

To achieve higher reliability, safety, and fault-tolerance, many mission-critical detection and decision systems implement consensus algorithms that force the system´s underlying sensor networks to reach the states of consensus and unanimous decision among the sensor nodes. Most consensus algorithms presented in the literature utilize local averaging (for continuous values) and majority voting (for discrete values) operators combined with iterative message passing and other similar nearest-neighbor information propagation schemes. Although very simple to implement, such schemes can be very prone to noise because individual detection and decision errors can be amplified and propagated many times throughout the network. For this reason, in this paper we propose a novel consensus algorithm for binary systems that requires each sensor node to participate in message propagation only if its input exceeds a predetermined threshold. This algorithm is a solution to what we call The Chinese Generals Problem, a wide generalization of The Byzantine Generals Problem by Lamport et al [1]. The threshold function used in the algorithm leads to an adjustable network-wide threshold level that defines the minimum number of nodes initially reporting positive detection required in order for all the nodes to reach the correct consensus.